The Wilkinson polynomial is the degree-20 polynomial
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Its roots are the integers 1 through 20, but small perturbations of its expanded coefficients can move some roots by surprisingly large amounts or make them nonreal. Wilkinson used the example to demonstrate that recovering roots from polynomial coefficients can be an ill-conditioned problem even when the roots themselves are simple and well separated.
The example distinguishes the conditioning of the mathematical problem from the numerical stability of a particular root-finding algorithm.
